# Tubing Leak

## In this section, we describe the load case Tubing leak, available in Oliasoft WellDesign.#

Tubing leak is a burst load case, where the unknown is the internal pressure profile of the casing / tubing.

NOTE!
In this documentation we denote any tubular as casing or tubing. All calculations however encompass any tubular, such as tubings, casings, liners, tie-backs etc.

## Summary#

This load case is used in connection with production- and injection- operations, and represents a surface pressure on top of a completion fluid due to a tubing leak.

### Printable Version#

Oliasoft Technical Documentation - Tubing Leak

## Inputs#

The following inputs define the tubing leak load case

1. The true vertical depth (TVD) along the wellbore as a function of measured depth. Alternatively, the wellbore described by a set of survey stations, with complete information about measured depth and inclination.
2. The true vertical depth / TVD of
1. The hanger of the tubing, TVD$_{hanger}$
2. The shoe of the tubing, TVD$_{shoe}$
3. The packer depth, TVD$_{packer}$
4. The perforation depth, TVD$_{perforation}$
3. The pore pressure profile from hanger to influx depth.
4. The packer fluid density, $\rho_{packer}$
5. The temperature at the perforation depth, $T_{perforation}$
6. The gas gravity, $sg_{gas}$

Scenario Illustration

## Calculation#

The internal pressure profile of the casing / tubing is calculated as follows

1. Calculate the pore pressure at perforation depth, $p_{p,perforation}$

2. Calculate the gas density at perforation depth from gas gravity, using Sutton correlations, $\rho_{gas,perforation}$

3. Calculate the pressure at the hanger

$p_\text{hanger} = p_\text{p, perforation} - \rho_\text{gas, perforation}\, g\, (\text{TVD}_{\text{perforation}} - \text{TVD}_{\text{hanger}}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (1)$

where $g$ is the gravitational constant.

4. The internal pressure of the tubing depends on where the packer- and perforation- depth are related to each other and the shoe of the tubing. Explicitly, parametrize the tubing by TVD

1. If $\text{TVD}_\text{shoe} \leq \text{TVD}_\text{packer} \leq \text{TVD}_\text{perforation}$, or if $\text{TVD}_\text{shoe} \leq \text{TVD}_\text{perforation} \leq \text{TVD}_\text{packer}$, then

$p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (2)$

2. If $\text{TVD}_\text{packer} \leq \text{TVD}_\text{shoe} \leq \text{TVD}_\text{perforation}$, then from hanger to packer

$p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}), \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (3)$

and from packer to shoe

$p_i = p_\text{perforation} - \rho_\text{gas, perforation}\, g\, (\text{TVD}_\text{perforation} - \text{TVD}). \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (4)$

3. If $\text{TVD}_\text{packer} \leq \text{TVD}_\text{perforation} \leq \text{TVD}_\text{shoe}$, then from hanger to packer

$p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (5)$

from packer to perforation

$p_i = p_\text{perforation} - \rho_\text{gas, perforation}\, g\, (\text{TVD}_\text{perforation} - \text{TVD}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (6)$

and finally from perforation to shoe

$p_i = p_\text{perforation} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_\text{perforation}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (7)$

4. If 4.1 = 4.2, then from hanger to perforation

$p_i = p_\text{hanger} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_{\text{hanger}}) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(8)$

and from perforation to shoe

$p_i = p_\text{perforation} + \rho_\text{packer}\, g\, (\text{TVD} - \text{TVD}_\text{perforation}). \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ (9)$

5. The last scenario, $\text{TVD}_\text{perforation} \leq \text{TVD}_\text{packer} \leq \text{TVD}_\text{shoe}$, is physically impossible

## References#

[1] Curtis H. Whitson and Michael R. Brule ́. Phase behavior, volume 20 of Henry L. Doherty series. SPE Monograph series, 2000.

[2] Sutton, R.P.: “Compressibility Factors for High-Molecular Weight Reservoir Gases,” paper SPE 14265 presented at the 1985 SPE Annual, Technical Conference and Exhibition, Las Vegas, Nevada, 22–25 September.